# Algebra I/Content/Introduction to Basic Algebra Ideas/Exponents and Powers

Back to Table of Contents Algebra I

## Vocabulary

**Exponent** is a number written in superscript that denotes how many times the base will be multiplied by itself.
**Base** is the number to be multiplied by itself.

Example:
**Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 5^2=25}**

## Lesson

We use **exponents** to show when we're multiplying the same number more than one time.

- 3*3 = 3^2
- Three times three equals three to the second power (or three squared)

- 3*3*3 = 3^3
- Three times three times three equals three to the third power (or three cubed)

- 3*3*3*3= 3^4
- Three times three times three times three equal three to the fourth power

- 2*2*2 = 2^3
- Two times two times two equals two to the third power.

## Example Problems

Let's evaluate these expressions.

7^2

- Seven to the second power, or seven squared, means seven times seven.

7*7

- Seven times seven is forty-nine.

49

- So, seven to the second power equals forty-nine.

Area of a square = (length of the side) ^2

- The area, or space inside, of a square is equal to the length of the side of the square to the second power.

Area of a square with side length 3 meters

- If the square had a side length of 3 meters,

(3 meters)^2

- Then the area would be (3 meters) squared.

3*3 meters^2

- 3 squared is the same as 3 times 3.

9 meters^2

- So, the area of a square with a side length of 3 meters is 9 meters squared.

c^2 where c=6

- First, we replace the variable "c" in the expression with 6, which is what it equals.

6^2

- 6 squared equals 6 times 6.

6*6

- 6 times 6 equals 36.

36

- So, c squared is 36.

x^3 where x = 10.

- First, we replace the variable "x" in the expression with 10, which is what it equals.

10^3

- 10 to the third power, or 10 cubed, is equal to 10 times 10 times 10.

10*10*10

- 10 times 10 equals 100.

100*10

- 100 times 10 equals 1000.

1000

- So, x to the third power is 1000.

y^4 where y = 2

- First, we replace the variable "y" in the expression with 2, which is what it equals.

2^4

- 2 to the fourth power is equal to 2 times 2 times 2 times 2.

2*2*2*2

- 2 times 2 equals 4.

4*2*2

- 4 times 2 equals 8.

8*2

- And 8 times 2 equals 16.

16

- So, y to the fourth is 16.

## Practice Games

http://www.math.com/school/subject2/practice/S2U2L2/S2U2L2Pract.html

http://www.quia.com/pop/50485.html (scientific notation)

http://www.softschools.com/math/games/exponents_practice.jsp

http://www.quia.com/quiz/358716.html (King Kong Scientific Notation)

## Practice Problems

(Note: put answer in parentheses after each problem you write)

Evaluate the following expressions:

- 6^2 (36)
- 2^3 (8)
- 4^2 (16)
- 5^3 (125)
- 2^4 (16)
- 9^2 (81)
- 8^2 (64)